Available Reports:

Polynomial Approximation to the Inverse of a Large Matrix,  manuscript  2024 (with Mark Embree,  Joel Henningsen and Jordan Jackson).

PolyApprInverse

New Polynomial Preconditioned GMRES (since renamed to be “Toward Stable and Efficient Polynomial Preconditioned GMRES”) ,  manuscript  2019 (with Jennifer Loe).

NewPPGMRES

Polynomial Preconditioned Arnoldi with Stability Control,  SIAM J. Sci. Comput., vol. 43 (2021), pp. A1-A25 (with Mark Embree and Jennifer Loe).

PPArn

Two-grid Deflated Krylov Methods for Linear Equations,  manuscript  2018 (with Zhao Yang ).

2GridLE

Perturbed Arnoldi for Computing Multiple Eigenvalues,  manuscript 2016 (with Mark Embree and Thomas Gibson).

PertArnMEV

Weighted Inner Products for GMRES and GMRES-DR, SIAM J. Sci. Comput., vol. 39 (2017), pp. S610-S632, (with Mark Embree and Huy Nguyen).

GWeighted

Polynomial Preconditioned BiCGStab and IDR,  manuscript 2016 (with Jennifer Loe).

PPNonSymmLancLinEqs

Two-grid and Multiple-grid Arnoldi for Eigenvalues,  SIAM J. Sci. Comput., vol. 40 (2018), pp. A3470–A3494 (with Zhao Yang).

MGArnoldi

New Noise Subtraction Methods in Lattice QCD,  Proceedings of Science,  Vol: Lattice 2016, (2016) 6 pages (with Walter Wilcox and Suman Baral).

NoiseSub

 Pseudoeigenvector Bases and Deflated GMRES for Highly Nonnormal Matrices,  Numer. Linear Alg. Appl.  Applications, 23 (2016), pp. 1032-1045 (with Zhao Yang and Baojiang Zhong).

psevects

 Polynomial Preconditioned GMRES and GMRES-DR, SIAM J. Sci. Comput., 37 (2015), pp. S407-S428 (with Quan Liu and Walter Wilcox).

ppgmres

 Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides.  Numer. Linear Alg. Appl., vol. 21,  pp. 453-471, 2014 (with Abdou M. Abdel Rehim and Walter Wilcox).

seed

 GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning, SIAM. J. Matrix Anal. & Appl., vol. 34 , pp. 1066-1088, 2013 (with Josef A. Sifuentes and Mark Embree).

StabGMRES

 Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides, SIAM J. Sci. Comput., vol. 33, pp. 3037-3056, 2011 (with Dywayne Nicely).

nlandr

 Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-hand Sides, SIAM J. Sci. Comput., vol. 32, pp. 129-149, 2010 (with Abdou M. Abdel Rehim, Dywayne Nicely and Walter Wilcox).

landr

 Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides, Lin. Alg. Appl., vol. 429, pp. 2415-2434, 2008 (with Dean Darnell and Walter Wilcox).

gshift

 Complementary Cycles of Restarted GMRES, Numer. Linear Alg. Appl., vol. 15, pp. 559-571, 2008, (with Baojiang Zhong).

ccyc

 Deflated BiCGStab for linear equations in QCD
problems, Proceedings of Science LAT2007, pp. 026/1-026/7, 2007, (with Abdou M. Abdel-Rehim and Walter Wilcox).

Dbicgstab

 Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides, Manuscript originally 2004 and since rewritten (with Walter Wilcox).

gproj

 A Harmonic Restarted Arnoldi Algorithm for Calculating Eigenvalues and Determining Multiplicity, Lin. Alg. Appl., vol. 415, pp. 96-113, 2006.

harmArn

 Restarted Block GMRES with Deflation of Eigenvalues, Applied Numerical Mathematics, vol. 54, pp. 222-236, 2005.

bgdr

 Deflation of Eigenvalues for Iterative Methods in Lattice QCD, Nuclear Physics B (Proc. Suppl.), vol. 129, pp. 856-858, 2004 (with Dean Darnell and Walter Wilcox).

Lat2004

 Deflation of Eigenvalues for GMRES in Lattice QCD, Nuclear Physics B (Proc. Suppl.), vol. 106, pp. 1067-1069, 2002 (with Walter Wilcox).

qcd

 GMRES with Deflated Restarting. SIAM J. Sci. Comput., vol. 24, pp. 20-37, 2002.

gmresdr

 Preconditioning Eigenvalues and Some Comparison of Solvers. J. Comp. Appl. Math., vol. 123, pp. 101-116, 2000.

pre-evals

 Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations. SIMAX, vol. 21, pp. 1112-1135, 2000.

GMRES-IR

 Harmonic Projection Methods for Large Nonsymmetric Eigenvalue Problems. Num. Lin. Alg. Appl., vol. 5 pp. 33-55, 1998 (with Min Zeng).

ien

 On Restarting the Arnoldi Method for Large Nonsymmetric Eigenvalue Problems. Math Comp, vol. 65, pp. 1213-1230, 1996.

Arnoldi96

 A Restarted GMRES Method Augmented with Eigenvectors. SIMAX, vol. 16, pp. 1154-1171, 1995.

GMRES-E

 Preconditioning the Lanczos Algorithm for Sparse Symmetric Eigenvalue Problems. SIAM J. Sci. Comput, vol. 14, pp. 585-593, 1993 (with David Scott).

PL

 Computing Interior Eigenvalues of Large Matrices. Lin Alg Appl, vol. 154/156, pp. 289-309, 1991.

InterEvals

 Genalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices. SIAM J. Sci. Stat. Comput, vol. 7, pp. 817-825, 1986 (with David Scott).

GD

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